Robust White test with bootstrap and effect sizes¶

Source: R/robust_implementations.R · Help: ?performWhiteTestRobust

Extends performWhiteTest() with optional bootstrap resampling, confidence intervals, effect size reporting, and power analysis.

Usage¶

performWhiteTestRobust(
  model,
  data = NULL,
  method = c("standard", "reduced"),
  bootstrap = FALSE,
  B = 999,
  ci_level = 0.95,
  parallel = FALSE
)

Arguments¶

model: A fitted stats::lm object representing the mean specification to be diagnosed.
data: The data frame model was fitted to, or NULL, the default. The response, design, weights and offset are read from the fit itself, so a model that transforms its variables, has an offset() term, or takes its weights or offset from a column of the data needs no data, and the model frame of model is accepted as data (since 0.17.0; before, such models needed data). Data that are given are matched to the observations of the fit: rows with row names of their own by name, in any order; rows that only number themselves (a tibble, a data.table, a data frame whose row names were reset) by the row numbers of the fit, or in the order of the fit when they hold one row per observation. The rows the fit dropped may be there or not. Data whose rows cannot be shown to hold the observations of the fit are refused; see test_results.
method: Character string selecting the auxiliary specification. "standard" retains squares and cross-products, while "reduced" excludes cross-products for high-dimensional designs.
bootstrap: Logical, compute bootstrap diagnostics for the statistic and p-value? The bootstrap is bootstrapTestStatistic(), so on a fit returned by fitWLS() each replicate estimates the weights again, its default since 0.15.0. There is no argument to hold them fixed here; bootstrapTestStatistic() with reestimate_weights = FALSE does that.
B: Number of bootstrap replications when bootstrap = TRUE. Defaults to 999, at which a bootstrap p-value of the form (1 + #) / (B + 1) gives an exact test at the 5% and 1% levels; it was 1000 before 0.15.0. The value is recorded in robust_details$bootstrap$B whether or not the bootstrap runs.
ci_level: Confidence level for reported intervals.
parallel: Logical, allow parallel bootstrap evaluation when the parallel package is available. A seeded call gives the same result each time; see Parallel replicates in bootstrapTestStatistic().

Value¶

An object of class htest augmented with a robust_details list containing bootstrap, effect size, and power information.

Details¶

Provides enriched inference around the White test by combining bootstrap resampling (Efron & Tibshirani, 1993) with asymptotic approximations. The robust_details element summarises interval estimates, effect sizes, and power calculations to aid decision-making.

Supported models¶

It accepts an lm and a glm with the Gaussian family and the identity link, unweighted or with positive weights, a fitWLS() fit and, since 0.16.0, a rank-deficient fit, which it tests on the estimable part of its design: it gives the value of the same model fitted without the aliased columns. It refuses a glm of another family or link, a survey::svyglm() fit, a fit with a zero weight, a coefficient that is not finite for another reason, and data that lack rows or variables of the fit. An mgcv::gam() fit with penalised smooth terms is tested on its design, the basis of its smooths, as by performWhiteTest(), and refused with bootstrap = TRUE (since 0.17.0; before, the bootstrap refused every gam with an error of its own): each replicate fits that design again by least squares, which a penalised fit is not. A gam that is the least-squares fit of its design, as one whose smooth terms are all fixed (s(x, fx = TRUE)) or one without smooth terms, is bootstrapped too, as the lm() of that design (decisions 37 and 38 of the design of the model context). Which model each test accepts, and why, is set out in test_results, under Supported models.

References¶

White, H. (1980). A heteroskedasticity-consistent covariance matrix estimator and a direct test for heteroscedasticity. Econometrica, 48(4), 817–838.

Efron, B., & Tibshirani, R. J. (1993). An Introduction to the Bootstrap. Chapman & Hall.

Examples¶

data(mtcars)
mod <- lm(mpg ~ wt + qsec, data = mtcars)
performWhiteTestRobust(mod, mtcars, bootstrap = TRUE, B = 200)